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SamplerModel[]

represents the single-input, single-output model of a sampler.

SamplerModel[specs]

represents a sampler with specification specs.

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SamplerModel

SamplerModel[]

represents the single-input, single-output model of a sampler.

SamplerModel[specs]

represents a sampler with specification specs.

Details

  • SamplerModel is also known as a sampler or regular sampling.
  • SamplerModel is typically used to convert a continuous-time signal coming from sensors to a discrete-time signal used by a digital microcontroller or digital signal processor.
  • A sampler is the model of an operation that takes a continuous-time signal and samples it at periodic intervals to generate a discrete-time signal , where is the sampling period.
  • When simulating a system using InputOutputResponse that includes a SamplerModel, it will be a mixed continuous-time and discrete-time system. In that case, all discrete-time signals are treated as piecewise constant value and continuous-time signals.
  • The specification spec is an association and can have the following keys:
  • "InputVariables"{u[t]}input variables
    "OutputVariables"{y[t]}output variables
    "SamplingPeriod"1sampling period
    "SignalCount"1number of inputs and outputs
    "TemporalVariable"ttemporal variable
  • SamplerModel[…]["prop"] can be used to obtain various properties of the model.
  • The value of "prop" can be any of the keys in spec and the following:
  • "Properties"list of property names
    "PropertyAssociation"property names and values as an association
    "PropertyDataset"property names and values as a dataset
    {p1,p2,…}values of properties pi

Examples

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Basic Examples  (2)

A sampler model:

Wolfram Language code: SamplerModel[]

Its properties:

Wolfram Language code: %["PropertyDataset"]

Simulate the response of a sampler to a sinusoidal input:

Wolfram Language code: r = InputOutputResponse[SamplerModel[], Sin[t], {t, 0, 2π}]

Plot the input signal and the sampler's response:

Wolfram Language code: Plot[{Sin[t], r}, {t, 0, 2π}]

Scope  (9)

A single-input, single-output sampler model:

Wolfram Language code: SamplerModel[]

A sampler with 2 inputs and outputs:

Wolfram Language code: SamplerModel[<|"SignalCount" -> 2|>]

A sampler with custom properties:

Wolfram Language code: SamplerModel[<|"InputVariables" -> u[t], "OutputVariables" -> y[t], "TemporalVariable" -> t|>]
Wolfram Language code: %["Dataset"]

List all available properties:

Wolfram Language code: SamplerModel[Association["DiscreteVariables" -> {Subscript[, 1][t]}, "InputVariables" -> {u[t]}, "OutputVariables" -> {y[t]}, "InitialStateValues" -> {}, "TemporalVariable" -> t, "WhenEvent" -> Mod[t, 1] == 0, "WhenEventAction" -> {Subscript ... ent", "WhenEventAction", "StateEquations", "OutputExpressions", "SignalCount", "Type", "PropertyFunction", "SamplingPeriod", "SummaryItems"}], {"InputVariables", "OutputVariables", "SamplingPeriod", "SignalCount", "TemporalVariable"}]["Properties"]

Obtain a specific property:

Wolfram Language code: SamplerModel[Association["DiscreteVariables" -> {Subscript[, 1][t]}, "InputVariables" -> {u[t]}, "OutputVariables" -> {y[t]}, "InitialStateValues" -> {}, "TemporalVariable" -> t, "WhenEvent" -> Mod[t, 1] == 0, "WhenEventAction" -> {Subscript ... ent", "WhenEventAction", "StateEquations", "OutputExpressions", "SignalCount", "Type", "PropertyFunction", "SamplingPeriod", "SummaryItems"}], {"InputVariables", "OutputVariables", "SamplingPeriod", "SignalCount", "TemporalVariable"}]["SamplingPeriod"]

Obtain several properties:

Wolfram Language code: SamplerModel[Association["DiscreteVariables" -> {Subscript[, 1][t]}, "InputVariables" -> {u[t]}, "OutputVariables" -> {y[t]}, "InitialStateValues" -> {}, "TemporalVariable" -> t, "WhenEvent" -> Mod[t, 1] == 0, "WhenEventAction" -> {Subscript ... ent", "WhenEventAction", "StateEquations", "OutputExpressions", "SignalCount", "Type", "PropertyFunction", "SamplingPeriod", "SummaryItems"}], {"InputVariables", "OutputVariables", "SamplingPeriod", "SignalCount", "TemporalVariable"}][{"SamplingPeriod", "SignalCount"}]

Obtain the properties as an association:

Wolfram Language code: SamplerModel[Association["DiscreteVariables" -> {Subscript[, 1][t]}, "InputVariables" -> {u[t]}, "OutputVariables" -> {y[t]}, "InitialStateValues" -> {}, "TemporalVariable" -> t, "WhenEvent" -> Mod[t, 1] == 0, "WhenEventAction" -> {Subscript ... ent", "WhenEventAction", "StateEquations", "OutputExpressions", "SignalCount", "Type", "PropertyFunction", "SamplingPeriod", "SummaryItems"}], {"InputVariables", "OutputVariables", "SamplingPeriod", "SignalCount", "TemporalVariable"}]["PropertyAssociation"]

As a dataset:

Wolfram Language code: SamplerModel[Association["DiscreteVariables" -> {Subscript[, 1][t]}, "InputVariables" -> {u[t]}, "OutputVariables" -> {y[t]}, "InitialStateValues" -> {}, "TemporalVariable" -> t, "WhenEvent" -> Mod[t, 1] == 0, "WhenEventAction" -> {Subscript ... ent", "WhenEventAction", "StateEquations", "OutputExpressions", "SignalCount", "Type", "PropertyFunction", "SamplingPeriod", "SummaryItems"}], {"InputVariables", "OutputVariables", "SamplingPeriod", "SignalCount", "TemporalVariable"}]["PropertyDataset"]

Simulate the response of a sampler to a decaying sinusoid:

Wolfram Language code: r1 = InputOutputResponse[SamplerModel[], inp = E^-tSin[ 4t], {t, 0, 8}]
Wolfram Language code: Plot[{inp, r1}, {t, 0, 8}, PlotRange -> All]

Decrease the sampling period to obtain better sampling:

Wolfram Language code: r2 = InputOutputResponse[SamplerModel[<|"SamplingPeriod" -> 0.25|>], inp, {t, 0, 8}]
Wolfram Language code: Plot[{inp, r2}, {t, 0, 8}, PlotRange -> All]

The lower sampling period results in better sampling:

Wolfram Language code: NIntegrate[Abs /@ {inp - r1[[1]], inp - r2[[1]]}, {t, 0, 8}]

Applications  (1)

A sampler model is a subsystem of a sampled data system:

Wolfram Language code: csys = SystemsConnectionsModel[{StateSpaceModel[{{{2}}, {{1}}, {{1}}, {{1}}}], StateSpaceModel[{{{0.951219512195122}}, {{-5.853658536585367, 6.829268292682928}}, {{0.009756097560975611}}, {{-0.029268292682926834, 0.03414634146341464}}}, Sampli ... OutputVariables", "SamplingPeriod", "SignalCount", "TemporalVariable"}]}, {{5, 1} -> {4, 1}, {4, 1} -> {6, 1}, {4, 1} -> {2, 1}, {6, 1} -> {1, 1}, {1, 1} -> {7, 1}, {7, 1} -> {2, 2}, {2, 1} -> {3, 1}, {3, 1} -> {4, 2}}, {{5, 1}}, {{1, 1}}];

Simulate the system:

Wolfram Language code: or = InputOutputResponse[csys, UnitBox[t - 0.5], {t, 0, 5}]

Plot the response:

Wolfram Language code: Plot[or, {t, 0, 5}, PlotRange -> All]

Properties & Relations  (4)

A sampler model is essentially a zero-order interpolation with zero initial values:

Wolfram Language code: u = Cos[t]; sp = 0.5;

The interpolation:

Wolfram Language code: Join[{{0, 0}}, Table[{t, u}, {t, sp, 2π, sp}]]; r1 = Interpolation[%, t - sp, InterpolationOrder -> 0]

The response of the sampler model:

Wolfram Language code: r2 = InputOutputResponse[SamplerModel[<|"SamplingPeriod" -> sp|>], u, {t, 0, 2π}]

They are the same:

Wolfram Language code: Plot[{r1, r2}, {t, 0, Round[2π]}]

A sampler model is essentially a time-based action:

Wolfram Language code: u = Cos[t]; sp = 0.5;

The response based on WhenEvent:

Wolfram Language code: r1 = NDSolveValue[{WhenEvent@@{Mod[t, sp] == 0, y[t] -> u}, y[0] == 0, Derivative[1][$][t] == 0, $[0] == 0}, y[t], {t, 0, 2 π}, DiscreteVariables -> {y[t]}]

The response of the sampler model:

Wolfram Language code: r2 = InputOutputResponse[SamplerModel[<|"SamplingPeriod" -> sp|>], u, {t, 0, 2π}]

They are the same:

Wolfram Language code: Plot[{r1, r2}, {t, 0, 2π}]

A holder model inverses the operation of a sampler model:

Wolfram Language code: f = 3; u = Sin[3 t]; sp = 1 / (100 f);

A sampler model in series with a holder model:

Wolfram Language code: sys = SystemsConnectionsModel[{SamplerModel[<|"SamplingPeriod" -> sp|>], HolderModel[<|"SamplingPeriod" -> sp|>]}, {{1, 1} -> {2, 1}}, {{1, 1}}, {{2, 1}}]

The output signal is the same as the input signal:

Wolfram Language code: InputOutputResponse[sys, u, {t, 0, 2π}]; Plot[{u, %[[1]]}, {t, 0, 2π}]

The Nyquist–Shannon sampling theorem says that the sampling frequency must be at least twice that of the input signal frequency to reconstruct the input signal from the sampled signal:

Wolfram Language code: f = 3; u = Sin[f t];

A function that connects a sampler model and a holder model in series:

Wolfram Language code: sys[sp_] := SystemsConnectionsModel[{SamplerModel[<|"SamplingPeriod" -> sp|>], HolderModel[<|"SamplingPeriod" -> sp|>]}, {{1, 1} -> {2, 1}}, {{1, 1}}, {{2, 1}}]

The output signal when the input is sampled at 10 times the frequency of the input signal:

Wolfram Language code: InputOutputResponse[sys[1 / (10 f)], u, {t, 0, 2π}]; Plot[{u, %[[1]]}, {t, 0, 2π}]

Sampling at 0.5 times the input frequency results in a poor reconstruction of the signal:

Wolfram Language code: InputOutputResponse[sys[1 / (0.5 f)], u, {t, 0, 2π}]; Plot[{u, %[[1]]}, {t, 0, 2π}]
Wolfram Research (2024), SamplerModel, Wolfram Language function, https://reference.wolfram.com/language/ref/SamplerModel.html.

Text

Wolfram Research (2024), SamplerModel, Wolfram Language function, https://reference.wolfram.com/language/ref/SamplerModel.html.

CMS

Wolfram Language. 2024. "SamplerModel." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SamplerModel.html.

APA

Wolfram Language. (2024). SamplerModel. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SamplerModel.html

BibTeX

@misc{reference.wolfram_2026_samplermodel, author="Wolfram Research", title="{SamplerModel}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/SamplerModel.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_samplermodel, organization={Wolfram Research}, title={SamplerModel}, year={2024}, url={https://reference.wolfram.com/language/ref/SamplerModel.html}, note=[Accessed: 13-June-2026]}